I have this statement on Taylor's Theorem in notes :
Let $U$ be an open set in $\mathbb R^n$ . Let $f\in C^{m+1}(U,\mathbb R)$.Let $x\in U$ and choose $r\gt 0$ such that $B(x,r) \subseteq U$.Then for $y\in \mathbb R^n$ such that $\|y\|\lt r$ , there is $t\in (0,1)$ such that
$$f(x+y) = f(x)+Df(y)+\frac{1}{2}D^2f(y,y)+\frac{1}{3!}D^3f(y,y,y)+...$$
Geometrically , $x+th$ means a point on the line segment joining $x$ and $x+h$ as $x+th=(1-t)x+t(x+h)$
I can't understand what the statement means..can anyone explain it to me..
Thanks in advance..